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Question:

A wheel with 8 metallic spokes each 50 cm long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of the Earth's magnetic field. The Earth's magnetic field at the place is 0.4G and the angle of 60°. Calculate the emf induced between the axle and the rim of the wheel. How will the value of emf be affected if the number of spokes were increased?

Solution:

H = Bcosθ = 0.4 × cos60° = 0.2G = 0.2 × 10⁻⁴T which is parallel to the plane of the wheel.
The emf induced is
E = ½Bl²ω
where ω = 2πN
E = ½ × 0.2 × 10⁻⁴ × (0.5)² × 2 × 3.14 × 120/60 = 3.14 × 10⁻⁵V
The emf induced is independent of the number of spokes as the emfs across them are in parallel. So it is unaffected by the increase in the number of spokes.